Arratia, [Arratia, R. (1979) Ph.D. thesis (University of Wisconsin, Madison) and unpublished work] and later Toth and Werner [Toth, B. & Werner, W. (1998) Probab. Theory Relat. Fields 111, 375-452] constructed random processes that formally correspond to coalescing one-dimensional Brownian motions starting from every space-time point. We extend their work by constructing and characterizing what...

Following an approach introduced by Lagnado and Osher (1997), we study Tikhonov regularization applied to an inverse problem important in mathematical finance, that of calibrating, in a generalized Black–Scholes model, a local volatility function from observed vanilla option prices. We first establish W 1,2 p estimates for the Black–Scholes and Dupire equations with measurable ingredients. Appl...

Throughout this paper, we always assume thatH is a real Hilbert space, whose inner product and norm are denoted by 〈·, ·〉 and ‖ · ‖. The symbols → and ⇀ are denoted by strong convergence and weak convergence, respectively. ωw xn {x : ∃xni ⇀ x} denotes the weak w-limit set of {xn}. Let C be a nonempty closed and convex subset of H and T : C → C a mapping. In this paper, we denote the fixed point...

Some optimal design problems in topology optimization eventually lead to a degenerate convex minimization problem E(v) := ∫ Ω W (∇v)dx − ∫ Ω f v dx for v ∈ H1 0 (Ω) with possibly multiple minimizers u, but with a unique stress σ := DW (∇u). This paper proposes the discrete Raviart–Thomas mixed finite element method (dRT-MFEM) and establishes its equivalence with the Crouzeix–Raviart nonconformi...

Because optical diffusion imaging is a highly nonlinear inverse problem, iterative inversion algorithms based on the Born approximation have usually been employed as reconstruction technique, but convergence is slow, especially for high contrast parameter distributions. We show here that the slow convergence of the conventional algorithms is due to the linear integral operator derived by the Bo...

where f IR IR is called the objective function and the set M the feasible region If the objective function possesses several local minima the determination of the global or lowest local minimum is an unsolvable problem in general p In this paper we are interested mainly in convergence speed of ESs such that we shall assume for simplicity that f has only one local minimum which is of course the ...

Consider the singular perturbation problem for εu(t; ε) + u(t; ε) = Au(t; ε) + ∫ t 0 K(t− s)Au(s; ε) ds+ f(t; ε) , where t ≥ 0, u(0; ε) = u0(ε), u (0; ε) = u1(ε), and w(t) = Aw(t) + ∫ t 0 K(t− s)Aw(s)ds+ f(t) , t ≥ 0 , w(0) = w0 , in a Banach space X when ε → 0. Here A is the generator of a strongly continuous cosine family and a strongly continuous semigroup, and K(t) is a bounded linear opera...

We consider the problem of estimating the slope parameter in functional linear instrumental regression, where in the presence of an instrument W , i.e., an exogenous random function, a scalar response Y is modeled in dependence of an endogenous random function X. Assuming second order stationarity jointly for X and W a nonparametric estimator of the functional slope parameter and its derivative...

Let the random (stock market) vector X 2 0 be drawn according to a known distribution function F(x), x E R ". A log-optimal portfolio b* is any portfolio b achieving maximal expected log return W* = sup,, E In b'X, where the supremum is over the simplex b 2 0, Cr, b, = 1. An algorithm is presented for finding b*. The algorithm consists of replacing the portfolio b by the expected portfolio b', ...

The paper studies empirically the time-space trade-off between sampling and inference in the cutset sampling algorithm. The algorithm samples over a subset of nodes in a Bayesian network and applies exact inference over the rest. As the size of the sampling space decreases, requiring less samples for convergence, the time for generating each single sample increases. Algorithm wcutset sampling s...